Explanation:

Let's break down the pattern step by step:

- 6789 : 34

- Add up the digits: 6+7+8+9 = 30

- Subtract the first digit from the sum: 30 - 6 = 24 (but the answer given is 34)

- Let's try adding the first and last, then the middle two: (6+9) + (7+8) = 15 + 15 = 30

- Looking at the difference: 6789 - 34 = 6755 (doesn't connect clearly)

- Let's check 6*7 + 8*9 = 42 + 72 = 114 (doesn't match)

- Try summing alternate digits: 6+8=14, 7+9=16, 14+16=30. No match.

- Let's check the difference between first two digits and last two: (67-89) = -22. Not matching.

- Try sum of first two and last two: 6+7=13, 8+9=17. 13+17=30.

- Try concatenation or subtraction?

- 1786 : 26

- Add up: 1+7+8+6 = 22. No match.

- 17+86 = 103

- 1*7 + 8*6 = 7 + 48 = 55

- 1+8=9, 7+6=13, 9+13=22

- Let's try (first digit × last digit) + (second digit × third digit): (1×6) + (7×8) = 6 + 56 = 62 (reverse is 26)

- 4327 : ?

- Use the above pattern: (first digit × last digit) + (second digit × third digit)

- (4×7) + (3×2) = 28 + 6 = 34

- Reverse 34 is 43

- Let's verify with original terms:

- 6789: (6×9) + (7×8) = 54 + 56 = 110, Reverse: 011 (no match)

- Let's check (first two digits × last two digits): 67×89 = 5963; 17×86=1462; 43×27=1161.

- Let’s try summing squares:

- 6²+7²+8²+9² = 36+49+64+81=230 (no)

- 1²+7²+8²+6²=1+49+64+36=150 (no)

- 4²+3²+2²+7²=16+9+4+49=78 (no)

- Let’s look at the gap between numbers:

- 6789-34=6755, 1786-26=1760, 4327-?

- Since none of these fit, it might be the sum of products of pairs:

- (6+7+8+9) = 30; difference from 34 is 4, but not matching with other terms.

- Is there a way the answer is 20? Let's check.

Best possible pattern seems to be:

- The two digits, added: for 43+27=70.

- Or sum of pairs: 4+3=7, 2+7=9, total=16.

- None seem to fit 20, 25, 30, or 35.

Pattern found:

Let's check the sum of extreme digits and central digits:

- 6789: (6+9) = 15; (7+8) = 15; 15 + 15 = 30

- 1786: (1+6)=7, (7+8)=15, total=22

- 4327: (4+7)=11, (3+2)=5, total=16

*Double-checking alternates:*

- Is answer options related to sum of digits × 2?

- 6789: (6+7+8+9)=30×2=60 (no match)

- Or adding digits and minus 2, etc.

Since no clear pattern emerges matching 26, 34, let’s focus:

- Given the pattern of reversing, see if for 34 -> 43, 26->62, so for 4327, if sum is 34 reverse is 43, otherwise, no.

Options:

1. 25

2. 20

3. 30

4. 35

Based on patterns attempted above, none exactly match, but since option 3 (30) seems related to adding digits in example 1, and that solution makes the most sense:

- 6+7+8+9 = 30, output is 34.

- 1+7+8+6 = 22, output is 26.

- 4+3+2+7 = 16, so adding 4 gives you 20 (option 2).

- But from examples, output is obtained by adding 4.

Thus, for 4327:

- 4+3+2+7=16

- 16+4=20 (option 2)

Option 2: 20 is correct.